Continuous and discontinuous transitions to synchronization

TL;DR

This paper investigates how the transition to synchronization in coupled Stuart-Landau oscillators shifts from continuous to discontinuous when changing the coupling from diffusive to reactive, revealing new macrostate coexistence phenomena.

Contribution

It demonstrates the qualitative change in synchronization transition types due to coupling nature and introduces the coexistence of synchronized and incoherent states at the transition.

Findings

Discontinuous transition occurs with reactive coupling.

Coexistence of synchronized and incoherent states at transition.

Finite size effects and connections to recent observations are discussed.

Abstract

We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the later is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exist at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.